Datasets categorized per figure and contain data in x,y format. for the DFT part: 35 elementary steps were studied. Each step is marked RX_NEB_InitialState_FinalState, and corresponds to the neb calculation for the identification of the transition state. In each file, POSCAR_00 corresponds to the initial structure and POSCAR_09 to the final structure, in both cases after geometry optimization. In each state, a file with the vibration calculation for the calculation of the Gibbs Energy is included. The Gibbs energies of the initial, transition and final states in table format are provided in Figure 4 - panel b - Gibbs Energies_Initial_Transition_Final_states_35_elementary_reactions The calculation of Gibbs energies of the gas phase molecules in the empty unit cell, used as reference states are provided in Figure 4 - Reference_state_Gases_empty_unit_cell The computations for the comparison of the different sites (HMo, Hc, atop and bridge) are provided in Table S6 - Comparison_adsorption_sites The computations on the model with a partial oxygen coverage (O.67 O ML) are provided in: Figure S29 - mo2c-ctx-3x3_067OML_C_CH_CCH Figure S29 - mo2c-ctx-3x3_067OML_CH3_H_CH4 Figure S29 - mo2c-ctx-3x3_067OML_CO_C_O Figure S29 - mo2c-ctx-3x3_067OML_CO_O_CO2